Aims. The study of the morphology of coronal mass ejections (CMEs) is an auspicious approach to understanding how magnetic fields are structured within CMEs. Although earlier studies have suggested an asymmetry in the width of CMEs in orthogonal directions, this has not been inspected using multi-viewpoint observations. Methods. We inspect the early evolution (below ten solar radii) of the morphology of a dozen CMEs occurring under specific conditions of observing spacecraft location and CME trajectory, favorable to reduce uncertainties typically involved in the 3D reconstruction used here. These events are carefully reconstructed by means of a forward modeling tool using simultaneous observations of STEREO EUVI and SDO/AIA as input when originating low in the corona, and followed up in the outer fields of view of the STEREO and the SOHO coronagraphs. We then examine the height evolution of the morphological parameters arising from the reconstructions. Results. The multi-viewpoint analysis of this set of CMEs revealed that their initial expansion --below three solar radii-- is considerably asymmetric and non-self-similar. Both angular widths, namely along the main axes of CMEs ($AW_L$) and in the orthogonal direction ($AW_D$, representative of the flux rope diameter), exhibit much steeper change rates below this height, with the growth rate of $AW_L$ found to be larger than that of $AW_D$, also below that height. Angular widths along the main axes of CMEs are on average $approx$1.8 times larger than widths in the orthogonal direction $AW_D$. The ratios of the two expansion speeds, namely in the directions of CMEs main axes and in their orthogonal, are nearly constant in time after $sim$4 solar radii, with an average ratio $approx$1.6. Heights at which the width change rate is defined to stabilize are greater for $AW_L$ than for $AW_D$.
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